mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

, the diagrammatic Monte Carlo method is based on stochastic summation of

Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduc ...

s with controllable error bars. It was developed by Boris Svistunov and

Nikolay Prokof'ev Nikolay Victorovich Prokof'ev is a Russian-American physicist known for his works on supersolidity and strongly correlated systems and pioneering numerical approaches. Biography He received his MSc in physics in 1982 from Moscow Engineering Phys ...

. It was proposed as a generic approach to overcome the

numerical sign problem In applied mathematics, the numerical sign problem is the problem of numerically evaluating the integral of a highly oscillatory function of a large number of variables. Numerical methods fail because of the near-cancellation of the positive and neg ...

that precludes simulations of many-body fermionic problems. Diagrammatic Monte Carlo works in the thermodynamic limit, and its computational complexity does not scale exponentially with system or cluster volume.

References

Monte Carlo methods Mathematical physics Quantum mechanics {{quantum-stub